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### On separable self-complementary graphs

Ken-ichi Kawarabayashi, Atsuhiro Nakamoto, Yoshiaki Oda, Katsuhiro Ota, Shinsei Tazawa, Mamoru Watanabe
2002 Discrete Mathematics
In this paper, we describe the structure of separable self-complementary graphs.  ...  The number of the separable self-complementary graphs with n¿8 vertices is the same as the number of the self-complementary graphs with n − 4 vertices.  ...  A graph G is said to be trivial if G has just one vertex, and G is empty if G has no vertex. A graph G is said to be separable if G has a cut vertex.  ...

### Page 4930 of Mathematical Reviews Vol. , Issue 2003g [page]

2003 Mathematical Reviews
separable self-complementary graphs.  ...  Using this result and the known enumeration of self-complementary graphs, the authors are able to enumerate all separable self- complementary graphs, by proving that the number of separable self-complementary  ...

### Page 508 of Mathematical Reviews Vol. , Issue 80B [page]

1980 Mathematical Reviews
Author’s summary: “We describe an algorithm for generating self-complementary graphs.  ...  The author obtains an asymptotic formula for the number of self-complementary oriented graphs. 80b:05037 R. C. Read (Waterloo, Ont.)  ...

### Page 8406 of Mathematical Reviews Vol. , Issue 2000m [page]

2000 Mathematical Reviews
In this se- ries of papers, the self-complementary 2-multigraphs are studied in detail because the fundamental graph of a self-complementary di- graph is a self-complementary 2-multigraph.  ...  (The case k = 4 and n > 10 was proved separately by the authors [J. Graph Theory 29 (1998), no. 2, 63- 72; MR 2000g:05055].)  ...

### Some New Classes of Open Distance-Pattern Uniform Graphs

Bibin K. Jose
2013 International Journal of Combinatorics
We also characterize odpu-self-complementary graphs, odpu-distance-hereditary graphs, and odpu-cographs.  ...  We prove that the odpu-number of cographs is even and establish that any graph G can be embedded into a self-complementary odpu-graph H, such that G and G¯ are induced subgraphs of H.  ...  , self-complementary graphs, 4 -free graphs, maximal outerplanar graphs, ptolemaic graphs, and distance-hereditary graphs.  ...

### On almost self-complementary graphs

Primož Potočnik, Mateja Šajna
2006 Discrete Mathematics
In particular, we give necessary and sufficient conditions on the order of an almost self-complementary regular graph, and construct infinite families of almost self-complementary regular graphs, almost  ...  A graph is called almost self-complementary if it is isomorphic to one of its almost complements X c − I, where X c denotes the complement of X and I a perfect matching (1-factor) in X c .  ...  focus on homogeneously almost self-complementary graphs.  ...

### Self-Attention Equipped Graph Convolutions for Disease Prediction [article]

Anees Kazi , Karsten Kortuem Computer Aided Medical Procedures, Technische Universit Munchen, Germany, National Institute of Technology Tiruchirappalli, India, Sharif University of Technology, Iran, Augenklinik der Universitat, Klinikum der Universitat Munchen, Germany, Johns Hopkins University, Baltimore MD, USA)
2018 arXiv   pre-print
Such diverse data gives complementary information about the patient\'s condition to make an informed diagnosis.  ...  We propose a graph convolution based deep model which takes into account the distinctiveness of each element of the multi-modal data.  ...  The method proposes to use each demographic information separately to construct a neighborhood graph.  ...

### Self-complementary and self-converse oriented graphs

M.R. Sridharan
1970 Indagationes Mathematicae (Proceedings)
In this paper we extend these results to obtain the formula for the number of selfcomplementary oriented graphs on n points and the generating function for selfconverse oriented graphs in terms of the  ...  Suitable modifications of the same scheme gave HARARY and PALMF,R [4], [5] the basic clue for their enumeration of self-converse digraphs.  ...  The number of self-complem entary oriented graphs is Y n =~L zO,,On(tX) ,-: L ij; + L L (q, r) jqjr . Fig. 1 . 1 Self-complementary oriented graphs with five points.  ...

### Exclusivity principle forbids sets of correlations larger than the quantum set

Barbara Amaral, Marcelo Terra Cunha, Adán Cabello
2014 Physical Review A. Atomic, Molecular, and Optical Physics
Moreover, we prove that, for self-complementary graphs, the E principle, by itself (i.e., without further assumptions), excludes any set of correlations strictly larger than the quantum set.  ...  We show that the exclusivity (E) principle singles out the set of quantum correlations associated to any exclusivity graph assuming the set of quantum correlations for the complementary graph.  ...  Such duality gets stronger when G is a self-complementary graph. A graph G is self complementary when G and G are isomorphic.  ...

### Page 6771 of Mathematical Reviews Vol. , Issue 98K [page]

1998 Mathematical Reviews
A graph is called self-complementary if it is isomorphic to its own complement.  ...  Jean-Claude Bermond (Sophia Antipolis) 98k:05119 05C75 05C25 Li, Cai Heng (5-WA; Nedlands) On self-complementary vertex-transitive graphs. (English summary) Comm.  ...

### Page 3600 of Mathematical Reviews Vol. , Issue 2001F [page]

2001 Mathematical Reviews
|[Wong, Chiu-Kwong] (PRC-CHHK-CSE; Shatin) Self-complementary graphs and Ramsey numbers. I. The decomposition and construction of self-complementary graphs.  ...  Let G be a self-complementary graph on the vertex set {v;,U2,-++,UV4n}, where deg(v,) < deg(v2) < --- < deg(v,,).  ...

### Page 861 of Mathematical Reviews Vol. , Issue 85c [page]

1985 Mathematical Reviews
Then G is called a graph [digraph] realization of S. We characterize integer-pair sequences which have a self-complementary graph |di- graph; tournament] as a realization.  ...  We then give a unified ap- proach to characterizing integer-pair sequences as well as degree sequences which are graphic and have every graph realization self- complementary.” F.  ...

### Corrigendum to "Almost self-complementary factors of complete bipartite graphs" [Discrete Math. 167/168 (1997) 317–327]

Dalibor Fronček
2001 Discrete Mathematics
Let F 1 and F 2 be its almost self-complementary factors and : F 1 → F 2 the self-complementing isomorphism.  ...  Due to this missing assumption, one class of disconnected almost self-complementary factors ofK 2n+1; 2m+1 with isolated vertices was omitted. The Lemma was stated as follows: Lemma 1.4.  ...

### A family of non-Cayley cores based on vertex-transitive or strongly regular self-complementary graphs [article]

Marko Orel
2021 arXiv   pre-print
The same conclusion is obtained for many vertex-transitive self-complementary graphs.  ...  Given a finite simple graph Γ on n vertices its complementary prism is the graph ΓΓ̅ that is obtained from Γ and its complement Γ̅ by adding a perfect matching, where each its edge connects two copies  ...  Later during 8ECM he attended the talk of Paula Carvalho, where he learned that graph ΓΓ was introduced in [49] and is known as the 'complementary prism'.  ...

### The generalized split probe problem

Simone Dantas, Luerbio Faria, Celina M.H. de Figueiredo, Rafael B. Teixeira
2013 Electronic Notes in Discrete Mathematics
classes are self-complementary!  ...  Peng, On the recognition of probe graphs of some self-complementary classes of perfect graphs, COCOON 2005 Strong probe graph conjecture C probe graphs are polynomially recognizable whenever C is  ...  There may exist a graph class C for which the C partitioned probe problem is NP-complete whereas the C unpartitioned probe is polynomial Even more interesting would be a graph class C for which recognition  ...
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